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t^(x-1)e^(-atcos(b))cos(atsin(b))

with respect to t. specifically, i'm asked to solve in terms of the gamma function. my question is more of what general technique i should use. all i've been able to do so far is beat it to death using integration by parts, with several different choices for the parts. the main problem i see here is the trig function within the trig function. any insights?

thanks in advance.